stat help

[drist]

I have this question for a beginer stats class that I just might be over thinking
here it is
in 2009 a sample of employees of acertain busniess had a median annual salary of $42500. For 2010 each memeber of the sample is still working there, and they all recieve a pat raise of 2% as well as a one-of $750 perfromance bonus . what is the median salary for 2010 (including the bonus) ?

my thought is to take 2% of 42500 which is 850 add 750 which is 44100. Is that it?? is there something I am missing ??
any help would be great

 

[mmm4444bot]

I think that's correct.

The median is the middle.

In other words, we order all of the employees by income from smallest to largest. The person making $42,500 in 2009 happens to be in the center of this list. Half of everybody else earns more and the other half earns less.

Clearly, that position does not change, if we add $750 to everyone's income. Half of the remaining employees still earn less than ($42,500 + $750) and half of them still earn more because everybody's income went up by the same amount.

The added percentage doesn't change the median position, either. It just results in a bigger raise for the second half and a lesser raise for the first half.

I mean, none of the people in the first half will be able to surpass 2% of $42,500 because they all earn less than $42,500. They can't get out of the first half of the ordered list.

None of the people in the second half will drop into the first half because their 2% increase is always applied to more than $42,500.

Since it's the same people in front of and behind the person in the middle, that person's increased income remains the median for 2010.

I hope that makes sense. (It did when I typed it.)